In the Dark Knight Rises movie, Bruce Wayne visits the doctor and is diagnosed with cartilage problems. That is, he has no cartilage. Is the knee bracing device that he uses meant to heal the cartilage or brace the knee or both? Is it a real medical device?

There are devices like this that do exist in real life, actually. I myself have a knee brace that, although not having servo-motors that assist in forward movement/strength, is fastened by hand with Velcro and has metal joints in it.

It wouldn't take too much engineering (and from what I read, it isn't, because it's being done) to make a knee brace with servo-motorized joints that open and close to the normal range of the leg (so as not to hyper-extend it).

Now, as for Batman's stiff-kick that knocks the bricks out of the archway in the cave...I'm not sure how a motorized knee brace would help that. Kicks are thrown with the full body-weight behind it, having very little to do with the actual leg (although front kicks utilize some leg-strength, even those are about thrusting your hips behind the kick). Obviously, you need the leg to be strong enough so as not to buckle...but a brace would have probably been more effective on the leg he posted on, since it would have knocked him off his feet. If you've never kicked something hard, like a door, you have to kick it hard enough that it knocks you back, similar to how Bane's kick on Batman in their first fight did.

My feeling is, the leg brace brought him back to his previous ability, to where he could have kicked those bricks out regardless (of logic). He then used the assisted stability to workout and rebuild strength in the leg, to the point that he wouldn't need the brace anymore. Makes sense with the prison plot and also makes sense with Wayne having been docile "peeing in mason jars" inside of his mansion for several years, not getting enough exercise to keep his previously damaged leg (that he still could run on, after killing Dent, when he was in peak condition) capable of function.